How do you rationalize the denominator and simplify 10/root3(7)?

Sep 28, 2015

$\frac{10}{7} \sqrt[3]{49}$

Explanation:

$\frac{10}{\sqrt[3]{7}}$

color(white)("XXX")=10/root(3)(7)*root(3)(7)/root(3)(7)*root(3)(7)/(root(3)(7)

$\textcolor{w h i t e}{\text{XXX}} = \frac{10 {\left(\sqrt[3]{7}\right)}^{2}}{{\left(\sqrt[3]{7}\right)}^{3}}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{10 \left(\sqrt[3]{{7}^{2}}\right)}{7}$

$\textcolor{w h i t e}{\text{XXX}} = \frac{10 \left(\sqrt[3]{49}\right)}{7}$